207 research outputs found
Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction
Extinction of an epidemic or a species is a rare event that occurs due to a
large, rare stochastic fluctuation. Although the extinction process is
dynamically unstable, it follows an optimal path that maximizes the probability
of extinction. We show that the optimal path is also directly related to the
finite-time Lyapunov exponents of the underlying dynamical system in that the
optimal path displays maximum sensitivity to initial conditions. We consider
several stochastic epidemic models, and examine the extinction process in a
dynamical systems framework. Using the dynamics of the finite-time Lyapunov
exponents as a constructive tool, we demonstrate that the dynamical systems
viewpoint of extinction evolves naturally toward the optimal path.Comment: 21 pages, 5 figures, Final revision to appear in Bulletin of
Mathematical Biolog
Isochronal synchronization of delay-coupled systems
We consider small network models for mutually delay-coupled systems which
typically do not exhibit stable isochronally synchronized solutions. We show
that for certain coupling architectures which involve delayed self feedback to
the nodes, the oscillators become isochronally synchronized. Applications are
shown for both incoherent pump coupled lasers and spatio-temporal coupled fiber
ring lasers.Comment: 5 pages, accepted for publication in Physical Review
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